Derivation of multiple but finite number of imaginary eigenvalues for a two-layer diffusion-reaction problem

Diffusion-reaction problems occur commonly in heat and mass transfer analysis. In the particular case of a multilayer body under certain conditions, such are known to result imaginary eigenvalues that indicate divergence temperature/concentration field at large times. For small values reaction coefficient, past work has derived conditions which an eigenvalue may exist. This generalizes this by showing more than one, but not infinite exist one-dimensional two-layer diffusion-reaction problem. A systematic investigation eigenequation space is carried out order derive closed form expression for number any given It shown that, other parameters being fixed, larger coefficients, greater eigenvalues. However, unlike real eigenvalues, it never infinite. While presented body, similar techniques be applied general although derivation explicit equations challenging. Besides its theoretical importance, accounting problem discussed here clearly important ensure accuracy mathematical model. The present contributes towards systematically identifying nature problems.